Properties

Label 4.6.a
Level 4
Weight 6
Character orbit a
Rep. character \(\chi_{4}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 3
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 4.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(4))\).

Total New Old
Modular forms 4 1 3
Cusp forms 1 1 0
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)Dim.
\(-\)\(1\)

Trace form

\(q \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 54q^{5} \) \(\mathstrut -\mathstrut 88q^{7} \) \(\mathstrut -\mathstrut 99q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 54q^{5} \) \(\mathstrut -\mathstrut 88q^{7} \) \(\mathstrut -\mathstrut 99q^{9} \) \(\mathstrut +\mathstrut 540q^{11} \) \(\mathstrut -\mathstrut 418q^{13} \) \(\mathstrut -\mathstrut 648q^{15} \) \(\mathstrut +\mathstrut 594q^{17} \) \(\mathstrut +\mathstrut 836q^{19} \) \(\mathstrut +\mathstrut 1056q^{21} \) \(\mathstrut -\mathstrut 4104q^{23} \) \(\mathstrut -\mathstrut 209q^{25} \) \(\mathstrut +\mathstrut 4104q^{27} \) \(\mathstrut -\mathstrut 594q^{29} \) \(\mathstrut +\mathstrut 4256q^{31} \) \(\mathstrut -\mathstrut 6480q^{33} \) \(\mathstrut -\mathstrut 4752q^{35} \) \(\mathstrut -\mathstrut 298q^{37} \) \(\mathstrut +\mathstrut 5016q^{39} \) \(\mathstrut +\mathstrut 17226q^{41} \) \(\mathstrut -\mathstrut 12100q^{43} \) \(\mathstrut -\mathstrut 5346q^{45} \) \(\mathstrut -\mathstrut 1296q^{47} \) \(\mathstrut -\mathstrut 9063q^{49} \) \(\mathstrut -\mathstrut 7128q^{51} \) \(\mathstrut +\mathstrut 19494q^{53} \) \(\mathstrut +\mathstrut 29160q^{55} \) \(\mathstrut -\mathstrut 10032q^{57} \) \(\mathstrut -\mathstrut 7668q^{59} \) \(\mathstrut -\mathstrut 34738q^{61} \) \(\mathstrut +\mathstrut 8712q^{63} \) \(\mathstrut -\mathstrut 22572q^{65} \) \(\mathstrut +\mathstrut 21812q^{67} \) \(\mathstrut +\mathstrut 49248q^{69} \) \(\mathstrut -\mathstrut 46872q^{71} \) \(\mathstrut +\mathstrut 67562q^{73} \) \(\mathstrut +\mathstrut 2508q^{75} \) \(\mathstrut -\mathstrut 47520q^{77} \) \(\mathstrut -\mathstrut 76912q^{79} \) \(\mathstrut -\mathstrut 25191q^{81} \) \(\mathstrut +\mathstrut 67716q^{83} \) \(\mathstrut +\mathstrut 32076q^{85} \) \(\mathstrut +\mathstrut 7128q^{87} \) \(\mathstrut +\mathstrut 29754q^{89} \) \(\mathstrut +\mathstrut 36784q^{91} \) \(\mathstrut -\mathstrut 51072q^{93} \) \(\mathstrut +\mathstrut 45144q^{95} \) \(\mathstrut -\mathstrut 122398q^{97} \) \(\mathstrut -\mathstrut 53460q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
4.6.a.a \(1\) \(0.642\) \(\Q\) None \(0\) \(-12\) \(54\) \(-88\) \(-\) \(q-12q^{3}+54q^{5}-88q^{7}-99q^{9}+\cdots\)